Bayesian Probability The geometry of changing beliefs.pptx
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This document discusses Bayes' theorem and its application. It begins with the formula P(H|E)= [P(E|H) P(H)]/P(E) and an example of using it to calculate the probability of a scientist given they are a farmer. It then explains the terms in Bayes' theorem - P(H) is the prior probability of a hypothesis, P(E|H) is the likelihood, P(E) is the marginal probability of evidence, and P(H|E) is the posterior probability. It ends with a quote about the importance of thinking like Bayesians and updating knowledge with new information.
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- 3. Gopal Gopal is a very shy and withdrawn, invariably helpful but with very little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail. Seem bookish….. He might be a scientist. Scientist(90%) Farmer(10%) You Scientist Farmer
- 5. 200 4 20 1:20 1 0 P(Scientist given farmer ) = 4/(4+20) = 16.7%
- 6. P(H|E)= [P(E|H) P(H)]/P(E) Bayes’ rule P(H) = Probability of a hypothesis is true (before any evidence) P(E|H)= Probability of seeing the evidence if the hypothesis is true. P(E)= Probability of seeing the evidence. P(H|E)= Probability of hypothesis is true given some evidence.
- 8. What is the probability of the event “both children are girls” (B) conditional on the event “the older child is a girl” (G)?
- 9. “Critical thinking is an active and ongoing process. It requires that we all think like Bayesians, updating our knowledge as new information comes in.”
- 10. THANK YOU